Analytic approximate solutions for steady flow over a rotating disk in porous medium with heat transfer by homotopy analysis method

• Published in: Computers & fluids Vol. 54; pp. 1 - 9
• Main Authors: Rashidi, M.M., Mohimanian Pour, S.A., Hayat, T., Obaidat, S.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 30.01.2012; Elsevier
• Subjects: Approximation; Convergence; Differential equations; Exact sciences and technology; Exact solutions; Flows through porous media; Fluid dynamics; Fundamental areas of phenomenology (including applications); General theory; Heat transfer; Homotopy analysis method; Laminar flows; Low-reynolds-number (creeping) flows; Mathematical analysis; Mathematical models; Nonhomogeneous flows; Physics; Rotating disk; Rotating disks; Steady flow; System of nonlinear ordinary differential equations; System of nonlinear ordinary differential equations; Rotating disk; Homotopy analysis method; Convergence; Temperature distribution; Porous medium flow; Homotopy; Steady flow; Differential equations; Velocity distribution; Incompressible fluid; Viscous fluids; Analytical solution; Heat transfer
• ISSN: 0045-7930; 1879-0747
• DOI: 10.1016/j.compfluid.2011.08.001

► The homotopy analysis method is used to obtain the analytical solutions of flow. ► The analytic solutions of the system of nonlinear ODEs are constructed in the series form. ► The influence of the porosity parameter is discussed in detail. ► The validity of the obtained solutions is verified by the numerical results. In this paper, the homotopy analysis method (HAM) is applied to obtain the approximate analytical solutions of the steady flow over a rotating disk in porous medium with heat transfer. The analytic solutions of the system of nonlinear ordinary differential equations are constructed in the series form. The convergence of the obtained series solutions is carefully analyzed. The velocity and temperature profiles are shown and the influence of the porosity parameter is discussed in detail. The validity of the obtained solutions is verified by the numerical results (fourth-order Runge–Kutta method and shooting method).